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Stochastic differential equations with multi-Markovian switching. (English) Zbl 1266.60105

Summary: This paper is concerned with stochastic differential equations (SDEs) with multi-Markovian switching. The existence and uniqueness of solution are investigated, and the \(p\)th moment of the solution is estimated. The classical theory of SDEs with single Markovian switching is extended.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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[1] A. V. Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations, vol. 78 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 1989. · Zbl 0739.60102
[2] X. Mao and C. Yuan, Stochastic Differential Euations with Markovian Switching, Imperial College Press, London, UK, 2006. · Zbl 1254.91592
[3] G. Yin and X. Y. Zhou, “Markowitz’s mean-variance portfolio selection with regime switching: from discrete-time models to their continuous-time limits,” IEEE Transactions on Automatic Control, vol. 49, no. 3, pp. 349-360, 2004. · Zbl 1366.91148
[4] J. Buffington and R. J. Elliott, “American options with regime switching,” International Journal of Theoretical and Applied Finance, vol. 5, no. 5, pp. 497-514, 2002. · Zbl 1107.91325
[5] C. Zhu and G. Yin, “On competitive Lotka-Volterra model in random environments,” Journal of Mathematical Analysis and Applications, vol. 357, no. 1, pp. 154-170, 2009. · Zbl 1182.34078
[6] Q. Luo and X. Mao, “Stochastic population dynamics under regime switching,” Journal of Mathematical Analysis and Applications, vol. 334, no. 1, pp. 69-84, 2007. · Zbl 1113.92052
[7] X. Li, D. Jiang, and X. Mao, “Population dynamical behavior of Lotka-Volterra system under regime switching,” Journal of Computational and Applied Mathematics, vol. 232, no. 2, pp. 427-448, 2009. · Zbl 1173.60020
[8] X. Li, A. Gray, D. Jiang, and X. Mao, “Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching,” Journal of Mathematical Analysis and Applications, vol. 376, no. 1, pp. 11-28, 2011. · Zbl 1205.92058
[9] M. Liu and K. Wang, “Asymptotic properties and simulations of a stochastic logistic model under regime switching,” Mathematical and Computer Modelling, vol. 54, no. 9-10, pp. 2139-2154, 2011. · Zbl 1235.60099
[10] G. Hu and K. Wang, “Stability in distribution of competitive Lotka-Volterra system with Markovian switching,” Applied Mathematical Modelling, vol. 35, no. 7, pp. 3189-3200, 2011. · Zbl 1228.34088
[11] M. Liu and K. Wang, “Asymptotic properties and simulations of a stochastic logistic model under regime switching II,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 405-418, 2012. · Zbl 1255.60129
[12] Z. Wu, H. Huang, and L. Wang, “Stochastic delay logistic model under regime switching,” Abstract and Applied Analysis, vol. 2012, Article ID 241702, 26 pages, 2012. · Zbl 1251.34099
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